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 Chebyshevskii Sb., 2020, Volume 21, Issue 3, Pages 29–38 (Mi cheb925)

The hearts of weight structures are the weakly idempotent complete categories

M. V. Bondarko, S. V. Vostokov

Saint Petersburg State University (St. Petersburg)

Abstract: This paper proves that additive categories that occur as hearts of weight structures are precisely the weakly idempotent complete categories, that is, the categories where all split monomorphisms give direct sum decompositions. The work also gives several other conditions equivalent to weak idempotent completeness (some of them are completely new) and discusses weak idempotent completions of additive categories.

Keywords: weakly idempotent complete category, idempotent completion, weak retraction-closure, triangulated category, weight structure, heart.

 Funding Agency Grant Number Russian Science Foundation 16-11-00200 This work was funded by the Russian Science Foundation under grant no. 16-11-00200.

DOI: https://doi.org/10.22405/2226-8383-2018-21-3-29-38

Full text: PDF file (772 kB)

UDC: 539.3
Accepted:22.10.2020
Language:

Citation: M. V. Bondarko, S. V. Vostokov, “The hearts of weight structures are the weakly idempotent complete categories”, Chebyshevskii Sb., 21:3 (2020), 29–38

Citation in format AMSBIB
\Bibitem{BonVos20} \by M.~V.~Bondarko, S.~V.~Vostokov \paper The hearts of weight structures are the weakly idempotent complete categories \jour Chebyshevskii Sb. \yr 2020 \vol 21 \issue 3 \pages 29--38 \mathnet{http://mi.mathnet.ru/cheb925} \crossref{https://doi.org/10.22405/2226-8383-2018-21-3-29-38}